The present invention relates generally to an iterative method for merging or fusing data acquired from varying sources or sensors. More particularly, the present invention relates to an iterative method of merging ordinal data which results in a ratio measurement level merged value.
Ordinal data is data which defines an ordering or ranks data in some order. In general, some data point is ranked first, another is ranked second, yet another is ranked third, and so on. The ranking is done with respect to some established criterion or criteria. The ranking may be based on an objective measurement or may be made subjectively.
Ordinal data while relatively uncommon in the physical sciences, is ubiquitous in the social sciences, psychology, psychometrics, economics, business and marketing and, indeed, in any activity or field of inquiry where data is gathered through means other than direct measurement. This includes data generated through surveys, expert assessments, preference ratings and rankings and through myriad other assessments of ordering, ranking or rating. A very simple example is the following: it is common practice in market research to assess customer product or service satisfaction through ratings surveys. In these surveys, customers are asked to rate some product or service, often on a scale of 1 to 5, across a number of categories or input domains. The result is a large set of ordinal data or alternatively, a set of sets of ordinal data. In general, further processing is required to make the ordinal data meaningfully usable. In particular, it is often desirable or required that the ordinal data be merged in some fashion and that this merged value be amenable to further quantitative or mathematical manipulation. The latter requirement means that the ordinal data must be converted to a more measurement-like or quantitative form. More formally, this is the problem of generating ratio scale data from ordinal scale data.
One known analytic technique for merging received ordinal data {x1, . . . xn} is through computing a weighted geometric meanGM(x1, . . . xn)=w√{square root over (x1W1x2W2. . . xnWn)}where w=w1+. . . +wn is the sum of the weights w1 associated to the n ordinal values xi. The geometric mean is preferred over a weighted mean or average for merging ordinal data, since, unlike the average, the geometric mean is invariant under order preserving transformations of the data. This means that the order of the geometric means, computed over a collection of ordinal data sets, is unaffected by order preserving transformations of the raw data. The geometric mean is the only meaningful analytic approach to merging ordinal data (Roberts, F. S. in Handbooks in OR and MS, vol. 6, eds. S. M. Pollock et al., Elsevier Science, New York, 1994). However, the geometric mean does not convert ordinal scale data to ratio scale data. The present invention offers an approximate or iterative technique for simultaneously merging and converting ordinal data into a ratio measurement level scalar.
PCT international application number PCT/US98/27374, filed Dec. 23, 1998 and designating the United States, is incorporated herein by reference. The incorporated application discloses an energy minimization technique for classification, pattern recognition, sensor fusion, data compression, network reconstruction and signal processing. The incorporated application shows a data analyzer/classifier which comprises using a preprocessing step, an energy minimization step and a post processing step to analyze and classify data. In a particular embodiment, the energy minimization is performed using individual differences multidimensional scaling. However, the incorporated application does not disclose an effective tool for merging or fusion of ordinal data.
Accordingly, there is a need for an improved method and apparatus for processing ordinal data.